When applying the classical Chi-square test of goodness of fit, it is always assumed that the test statistic is chi square - distributed. Since this is true only for very large samples, some restrictions on the class frequencies have to be introduced. It is generally accepted that none of the expected frequencies should be less than ten, which makes this test useless for small and moderate samples. In order to eliminate these - from a practical viewpoint severe - restrictions, it is proposed to use the exact sampling distribution instead of the limiting chi square-distribution. When doing so, the test will be called the Eks-square test. Programs have been written for computing these distributions and the improvements attained have been stated. The possibilities of using the modified test statistic as a location, scale, and shape operator have been examined and illustrated by numerical examples. Several tables have been prepared.